Subgroups — #27098666

Order 12032.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257331	C₂	1	2	yes	maximal, complemented
2	#20256401	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256141	C₂	1	2	yes	maximal, complemented
4	#20255789	C₂	1	1	yes	maximal, characteristic, complemented
5	#20255755	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255735	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255586	C₂	1	2	yes	maximal, complemented
8	#20255406	C₂	1	2	yes	maximal, complemented
9	#20255346	C₂	1	2	yes	maximal, complemented
10	#20255074	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255074	C₂	1	1	yes	maximal, characteristic, complemented
12	D₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#20254039	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254030	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253960	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253592	C₂	1	2	yes	maximal, complemented
17	#20253577	C₂	1	2	yes	maximal, complemented
18	#20253531	C₂	1	2	yes	maximal, complemented
19	#20252365	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252258	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252235	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094043	C₂²	1	1	yes	characteristic
25	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
27	#15689858	C₂²	1	2	yes	complemented
28	#15689826	C₂²	1	2	yes	complemented
29	#15689821	—	2	2	no	—
30	#15689811	C₂²	1	2	yes	—
31	#15689800	—	2	2	no	—
32	#15689800	—	2	2	no	—
33	#15689776	C₂²	1	2	yes	complemented
34	#15689768	C₂²	1	2	yes	complemented
35	#15689768	C₂²	1	2	yes	complemented
36	#15689764	—	2	2	no	—
37	D₄×D₁₈₈	C₂²	1	2	yes	—
38	#15689747	C₂²	1	2	yes	complemented
39	#15689729	C₂²	1	2	yes	complemented
40	#15689722	—	2	2	no	—
41	#15689713	—	2	2	no	—
42	#15689660	C₂²	1	1	yes	characteristic
43	#15689658	C₂²	1	2	yes	complemented
44	#15689636	—	2	2	no	—
45	C₂×#13094009	—	2	2	no	—
46	#15689602	C₂²	1	2	yes	complemented
47	#15689595	C₂²	1	2	yes	complemented
48	C₄×D₄×D₄₇	C₂²	1	2	yes	complemented
49	#15689507	C₂²	1	1	yes	characteristic, complemented
50	#15689507	C₂²	1	1	yes	characteristic, complemented
51	#15689500	C₂²	1	1	yes	characteristic
52	#15689489	C₂²	1	2	yes	complemented
53	#15689485	C₂²	1	2	yes	complemented
54	#15689480	C₂²	1	2	yes	complemented
55	#15689467	C₂²	1	2	yes	complemented
56	#15689455	C₂²	1	2	yes	complemented
57	#15689449	C₂²	1	2	yes	complemented
58	#15689443	C₂²	1	2	yes	complemented
59	#15689438	C₂²	1	2	yes	complemented
60	#15689438	C₂²	1	2	yes	complemented
61	#15689427	C₂²	1	2	yes	complemented
62	#15689420	C₂²	1	2	yes	complemented
63	#15689400	C₂²	1	2	yes	complemented
64	#15689377	C₂²	1	2	yes	complemented
65	#15689370	C₂²	1	2	yes	complemented
66	#15689365	C₂²	1	1	yes	characteristic, complemented
67	#15689365	C₂²	1	1	yes	characteristic, complemented
68	#15689360	C₂²	1	1	yes	characteristic
69	#15689360	C₂²	1	1	yes	characteristic
70	#15689360	C₂²	1	1	yes	characteristic, complemented
71	#15689360	C₂²	1	1	yes	characteristic, complemented
72	#15689353	C₂²	1	2	yes	complemented
73	#15689339	C₂²	1	2	yes	complemented
74	#15689339	C₂²	1	2	yes	complemented
75	#15689338	C₂²	1	2	yes	complemented
76	#15689338	C₂²	1	2	yes	complemented
77	#15689324	C₂²	1	2	yes	complemented
78	#15689318	C₂²	1	2	yes	—
79	#15689275	C₂²	1	2	yes	complemented
80	#15689275	C₂²	1	2	yes	complemented
81	#15689269	C₂²	1	2	yes	complemented
82	#15689269	C₂²	1	2	yes	complemented
83	#15689258	C₂²	1	2	yes	—
84	#15689258	C₂²	1	2	yes	—
85	#15689254	C₂²	1	1	yes	characteristic, complemented
86	#15689234	C₂²	1	2	yes	complemented
87	#15689233	C₂²	1	2	yes	complemented
88	#15689232	C₂²	1	2	yes	complemented
89	#15689223	C₂²	1	2	yes	complemented
90	#15689222	C₂²	1	2	yes	complemented
91	#15689220	C₂²	1	2	yes	complemented
92	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
93	#15689217	C₂²	1	1	yes	characteristic, complemented
94	#15689210	C₂²	1	2	yes	complemented
95	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₃₇₆	C₂²	1	1	yes	characteristic, complemented
97	D₈×Dic₄₇	C₂²	1	1	yes	characteristic
98	#15689205	C₂²	1	1	yes	characteristic, complemented
99	#15689205	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10625334	C₂²	1	2	yes	complemented
101	#15689203	C₂²	1	2	yes	complemented
102	#15689200	C₂²	1	1	yes	characteristic, complemented
103	#15689193	C₂²	1	1	yes	characteristic
104	#15689193	C₂²	1	1	yes	characteristic, complemented
105	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
106	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
107	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
108	#15689183	C₂²	1	1	yes	characteristic, complemented
109	#15689183	C₂²	1	1	yes	characteristic, complemented
110	#15689179	C₂²	1	1	yes	characteristic, complemented
111	#15689160	C₂²	1	1	yes	characteristic, complemented
112	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
113	#107×D₄₇	C₂²	1	1	yes	characteristic, complemented
114	#15689126	C₂²	1	2	yes	complemented
115	#15689121	C₂²	1	2	yes	complemented
116	#102×D₄₇	C₂²	1	2	yes	complemented
117	#15689077	C₂²	1	1	yes	characteristic, complemented
118	#15689077	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#554	C₂²	1	2	yes	complemented
121	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#478	C₂²	1	2	yes	complemented
125	C₄₇×#478	C₂²	1	2	yes	complemented
126	C₄₇×#476	C₂²	1	2	yes	complemented
127	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
131	C₂×#10625354	—	2	2	no	—
132	C₂×#10625352	C₂³	1	2	yes	—
133	C₂²×D₁₈₈	—	2	2	no	—
134	C₂×D₄×D₄₇	C₂³	1	2	yes	—
135	C₂×D₄×D₄₇	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₇	—	2	2	no	—
137	#13094043	—	2	4	no	—
138	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
139	C₂×#10625325	C₂³	1	2	yes	—
140	C₂×#10625325	C₂³	1	2	yes	—
141	C₂×#10625335	C₂³	1	2	yes	—
142	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
143	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
144	C₂×D₃₇₆	C₂³	1	2	yes	—
145	C₂×#10625334	C₂³	1	2	yes	—
146	C₂×#10625334	C₂³	1	2	yes	—
147	D₈×D₄₇	—	2	4	no	—
148	D₈×D₄₇	—	2	4	no	—
149	C₂×#10625324	C₂³	1	1	yes	characteristic
150	C₂×#10625324	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
155	#13094021	C₂³	1	2	yes	—
156	#13094019	—	2	2	no	—
157	#13094019	—	2	2	no	—
158	#13094019	—	2	2	no	—
159	#13094019	—	2	2	no	—
160	#13094019	D₄	1	1	yes	characteristic
161	#13094019	D₄	1	1	yes	characteristic
162	#13094015	—	2	2	no	—
163	#13094015	D₄	1	1	yes	characteristic
164	#13094013	—	2	2	no	—
165	#13094013	—	2	2	no	—
166	#13094013	D₄	1	1	yes	characteristic
167	#13094012	C₂³	1	2	yes	—
168	#13094012	C₂³	1	2	yes	—
169	#13094009	—	2	2	no	—
170	#13094009	—	2	2	no	—
171	#13094009	—	2	2	no	—
172	#13094009	—	2	2	no	—
173	#13094009	—	2	2	no	—
174	#13094009	—	2	2	no	—
175	#13094009	—	2	2	no	—
176	#13094009	—	2	2	no	—
177	#13094009	—	2	2	no	—
178	#13094009	—	2	2	no	—
179	#13094009	D₄	1	1	yes	characteristic
180	#13094009	D₄	1	1	yes	characteristic
181	#13094008	—	2	2	no	—
182	#13094008	—	2	2	no	—
183	#13094004	C₂³	1	2	yes	—
184	#13094004	C₂³	1	2	yes	—
185	#13094000	—	2	2	no	—
186	#13094000	—	2	2	no	—
187	#13094000	D₄	1	1	yes	characteristic
188	#13093999	—	2	2	no	—
189	#13093999	—	2	2	no	—
190	#13093999	—	2	2	no	—
191	#13093999	D₄	1	1	yes	characteristic
192	#13093999	C₂³	1	2	yes	—
193	#13093999	C₂³	1	2	yes	—
194	#13093999	C₂³	1	2	yes	—
195	#13093999	C₂³	1	2	yes	—
196	#13093998	—	2	2	no	—
197	#13093998	—	2	2	no	—
198	#13093998	—	2	2	no	—
199	#13093994	—	2	2	no	—
200	#13093994	—	2	2	no	—
201	#13093994	—	2	2	no	—
202	#13093994	—	2	2	no	—
203	C₄×Dic₉₄	C₂³	1	2	yes	—
204	#13093989	C₂³	1	2	yes	—
205	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
206	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
207	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
208	C₄×D₁₈₈	C₂³	1	2	yes	—
209	C₄×D₁₈₈	C₂³	1	2	yes	—
210	D₄×Dic₄₇	C₂³	1	2	yes	—
211	#13093986	—	2	2	no	—
212	#13093986	—	2	2	no	—
213	#13093986	—	2	2	no	—
214	#13093986	C₂³	1	2	yes	—
215	#13093986	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₄₇	—	2	2	no	—
217	C₄×C₂²⋊D₄₇	—	2	2	no	—
218	C₄×C₂²⋊D₄₇	—	2	2	no	—
219	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
220	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
221	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
222	#13093982	—	2	2	no	—
223	#13093982	—	2	2	no	—
224	#13093982	C₂³	1	2	yes	—
225	#13093981	C₂³	1	1	yes	characteristic
226	#13093981	C₂³	1	1	yes	characteristic
227	#13093980	—	2	2	no	—
228	C₂×Dic₄₇⋊C₄	—	2	2	no	—
229	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
230	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
231	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
232	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
233	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
234	C₂²⋊C₄×D₄₇	—	2	2	no	—
235	C₂²⋊C₄×D₄₇	—	2	2	no	—
236	C₄²×D₄₇	C₂³	1	1	yes	characteristic
237	#13093958	C₂³	1	1	yes	characteristic
238	#13093957	C₂³	1	2	yes	—
239	#13093957	C₂³	1	2	yes	—
240	#13093955	C₂³	1	2	yes	—
241	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
242	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
243	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
244	#13093949	C₂³	1	2	yes	—
245	#13093947	C₂³	1	2	yes	—
246	#13093947	C₂³	1	2	yes	—
247	#13093947	C₂³	1	2	yes	—
248	#13093946	C₂³	1	2	yes	—
249	#13093946	C₂³	1	2	yes	—
250	#13093945	C₂³	1	2	yes	—
251	#13093944	C₂³	1	2	yes	—
252	#13093944	C₂³	1	2	yes	—
253	#13093944	C₂³	1	2	yes	—
254	#13093944	C₂³	1	2	yes	—
255	#13093944	C₂³	1	2	yes	—
256	#13093944	C₂³	1	2	yes	—
257	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
258	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
259	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
260	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
263	#13093935	C₂³	1	1	yes	characteristic
264	#13093935	C₂³	1	1	yes	characteristic
265	#13093934	C₂³	1	1	yes	characteristic
266	#13093934	C₂³	1	1	yes	characteristic
267	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
270	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
271	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
272	#125×C₄₇	C₂³	1	2	yes	—
273	#125×C₄₇	C₂³	1	2	yes	—
274	C₂²⋊Q₈×C₄₇	—	2	2	no	—
275	C₂²⋊Q₈×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₄₇	C₂³	1	2	yes	—
279	C₄×D₄×C₄₇	C₂³	1	2	yes	—
280	C₄×D₄×C₄₇	C₂³	1	2	yes	—
281	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
282	#107×C₄₇	C₂³	1	1	yes	characteristic
283	#107×C₄₇	C₂³	1	2	yes	—
284	#107×C₄₇	C₂³	1	1	yes	characteristic
285	#107×C₄₇	C₂³	1	1	yes	characteristic
286	#106×C₄₇	C₂³	1	2	yes	—
287	#106×C₄₇	C₂³	1	2	yes	—
288	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
291	#102×C₄₇	C₂³	1	2	yes	—
292	#102×C₄₇	C₂³	1	2	yes	—
293	#102×C₄₇	C₂³	1	2	yes	—
294	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₂³×D₄₇	—	2	2	no	—
298	C₂³×D₄₇	—	2	2	no	—
299	C₂×Q₈×C₄₇	—	2	2	no	—
300	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₄₇	—	2	2	no	—
303	C₂²×C₄×C₄₇	—	2	2	no	—
304	C₂²×C₄×C₄₇	—	2	2	no	—
305	C₂×C₂²⋊D₄₇	—	2	2	no	—
306	C₂×C₂²⋊D₄₇	—	2	2	no	—
307	C₂×C₂²⋊D₄₇	—	2	2	no	—
308	C₂²×Dic₄₇	—	2	2	no	—
309	C₂²×Dic₄₇	—	2	2	no	—
310	#10625354	—	8	4	no	—
311	#10625352	—	2	4	no	—
312	#10625352	—	4	2	no	—
313	D₄×D₄₇	—	2	4	no	—
314	D₄×D₄₇	—	2	4	no	—
315	D₄×D₄₇	—	4	2	no	—
316	D₄×D₄₇	—	4	2	no	—
317	C₂×D₁₈₈	—	2	2	no	—
318	C₂×D₁₈₈	—	2	2	no	—
319	C₂×D₁₈₈	—	2	2	no	—
320	C₂×D₁₈₈	—	2	2	no	—
321	C₂×D₁₈₈	—	2	2	no	—
322	C₂×D₁₈₈	—	2	2	no	—
323	C₂×D₁₈₈	—	8	4	no	—
324	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
325	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
326	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
327	C₂×D₁₈₈	C₂⁴	1	2	yes	—
328	C₂×D₁₈₈	C₂⁴	1	2	yes	—
329	C₂×C₄×D₄₇	—	2	2	no	—
330	C₂×C₄×D₄₇	—	2	2	no	—
331	C₂×C₄×D₄₇	—	2	2	no	—
332	C₂×C₄×D₄₇	—	2	2	no	—
333	C₂×C₄×D₄₇	—	2	2	no	—
334	C₂×C₄×D₄₇	—	2	2	no	—
335	C₂×C₄×D₄₇	—	8	4	no	—
336	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
337	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
338	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
339	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
340	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
341	C₂×Dic₉₄	C₂⁴	1	2	yes	—
342	D₈×C₄₇	#41	1	4	yes	complemented
343	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
347	C₄⋊C₄×C₄₇	—	2	2	no	—
348	C₄⋊C₄×C₄₇	—	2	2	no	—
349	C₄⋊C₄×C₄₇	—	2	2	no	—
350	C₄⋊C₄×C₄₇	—	2	2	no	—
351	C₄⋊C₄×C₄₇	—	2	2	no	—
352	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
358	C₂²⋊C₄×C₄₇	—	2	2	no	—
359	C₂²⋊C₄×C₄₇	—	2	2	no	—
360	C₂²⋊C₄×C₄₇	—	2	2	no	—
361	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
362	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
363	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
364	C₂²⋊Dic₄₇	—	2	2	no	—
365	#10625335	—	2	4	no	—
366	#10625334	—	2	4	no	—
367	#10625334	—	2	4	no	—
368	(C₂×D₄₇)⋊C₄	—	2	2	no	—
369	(C₂×D₄₇)⋊C₄	—	2	2	no	—
370	(C₂×D₄₇)⋊C₄	—	2	2	no	—
371	(C₂×D₄₇)⋊C₄	—	2	2	no	—
372	(C₂×D₄₇)⋊C₄	—	2	2	no	—
373	(C₂×D₄₇)⋊C₄	—	2	2	no	—
374	(C₂×D₄₇)⋊C₄	—	2	2	no	—
375	(C₂×D₄₇)⋊C₄	—	2	2	no	—
376	(C₂×D₄₇)⋊C₄	—	2	2	no	—
377	(C₂×D₄₇)⋊C₄	—	2	2	no	—
378	(C₂×D₄₇)⋊C₄	—	2	2	no	—
379	(C₂×D₄₇)⋊C₄	—	2	2	no	—
380	(C₂×D₄₇)⋊C₄	—	2	2	no	—
381	(C₂×D₄₇)⋊C₄	—	2	2	no	—
382	(C₂×D₄₇)⋊C₄	—	2	2	no	—
383	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
386	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
387	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
388	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
389	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
390	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
391	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
392	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄⋊Dic₄₇	—	2	2	no	—
394	C₄⋊Dic₄₇	—	2	2	no	—
395	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
396	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
397	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
398	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
399	Dic₄₇⋊C₄	—	2	2	no	—
400	Dic₄₇⋊C₄	—	2	2	no	—
401	Dic₄₇⋊C₄	—	2	2	no	—
402	Dic₄₇⋊C₄	—	2	2	no	—
403	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
405	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
406	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₄×Dic₄₇	—	2	2	no	—
408	C₄×Dic₄₇	—	2	2	no	—
409	C₄×Dic₄₇	—	2	2	no	—
410	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
415	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
417	Dic₁₈₈	—	2	2	no	—
418	D₃₇₆	—	2	2	no	—
419	D₃₇₆	—	2	2	no	—
420	D₃₇₆	—	4	2	no	—
421	#10625325	—	4	2	no	—
422	#10625325	—	4	2	no	—
423	#10625324	—	4	1	no	—
424	#10625324	—	4	1	no	—
425	C₈×D₄₇	—	2	2	no	—
426	C₈×D₄₇	—	2	2	no	—
427	C₈×D₄₇	—	2	2	no	—
428	C₈×D₄₇	—	4	1	no	—
429	C₂³×C₄₇	—	2	2	no	—
430	C₂²×D₄₇	—	2	2	no	—
431	C₂²×D₄₇	—	2	2	no	—
432	C₂²×D₄₇	—	4	4	no	—
433	C₂²×D₄₇	—	4	4	no	—
434	C₂²×D₄₇	—	4	4	no	—
435	C₂²×D₄₇	—	8	2	no	—
436	C₂²×D₄₇	—	8	2	no	—
437	C₂²×D₄₇	—	8	2	no	—
438	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₄₇	—	4	1	no	—
442	Q₈×C₄₇	—	8	2	no	—
443	D₄×C₄₇	—	2	2	no	—
444	D₄×C₄₇	C₂×#41	1	4	yes	—
445	C₂×C₄×C₄₇	—	2	2	no	—
446	C₂×C₄×C₄₇	—	2	2	no	—
447	C₂×C₄×C₄₇	—	2	2	no	—
448	C₂×C₄×C₄₇	—	8	2	no	—
449	C₂×C₄×C₄₇	—	8	2	no	—
450	C₂×C₄×C₄₇	—	8	2	no	—
451	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
458	C₂²⋊D₄₇	—	4	4	no	—
459	C₂²⋊D₄₇	—	4	4	no	—
460	C₂²⋊D₄₇	—	4	4	no	—
461	C₂×Dic₄₇	—	2	2	no	—
462	C₂×Dic₄₇	—	2	2	no	—
463	C₂×Dic₄₇	—	4	4	no	—
464	C₂×Dic₄₇	—	8	2	no	—
465	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
470	D₁₈₈	—	2	2	no	—
471	D₁₈₈	—	2	2	no	—
472	D₁₈₈	—	2	2	no	—
473	D₁₈₈	—	2	2	no	—
474	D₁₈₈	—	2	2	no	—
475	D₁₈₈	—	2	2	no	—
476	D₁₈₈	—	4	1	no	—
477	D₁₈₈	—	4	4	no	—
478	D₁₈₈	—	8	2	no	—
479	D₁₈₈	—	8	2	no	—
480	D₁₈₈	—	8	2	no	—
481	D₁₈₈	—	8	2	no	—
482	D₁₈₈	—	8	2	no	—
483	C₄×D₄₇	—	2	2	no	—
484	C₄×D₄₇	—	2	1	no	—
485	C₄×D₄₇	—	2	1	no	—
486	C₄×D₄₇	—	2	1	no	—
487	C₄×D₄₇	—	2	1	no	—
488	C₄×D₄₇	—	2	1	no	—
489	C₄×D₄₇	—	2	1	no	—
490	C₄×D₄₇	—	4	1	no	—
491	C₄×D₄₇	—	4	4	no	—
492	C₄×D₄₇	—	8	2	no	—
493	C₄×D₄₇	—	8	2	no	—
494	C₄×D₄₇	—	8	2	no	—
495	C₄×D₄₇	—	8	2	no	—
496	C₄×D₄₇	—	8	2	no	—
497	Dic₉₄	—	2	2	no	—
498	Dic₉₄	—	2	2	no	—
499	C₈×C₄₇	—	2	1	no	—
500	C₈×C₄₇	—	2	1	no	—
501	C₈×C₄₇	—	2	1	no	—
502	C₈×C₄₇	C₂×#41	1	2	yes	—
503	C₄₇⋊C₈	—	2	1	no	—
504	C₄₇⋊C₈	—	2	1	no	—
505	C₄₇⋊C₈	—	2	1	no	—
506	C₄₇⋊C₈	—	2	1	no	—
507	#61471	—	47	1	no	maximal, Sylow
508	C₂²×C₄₇	—	2	4	no	—
509	C₂²×C₄₇	—	4	2	no	—
510	C₂²×C₄₇	—	4	2	no	—
511	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
512	C₂×D₄₇	—	2	1	no	—
513	C₂×D₄₇	—	2	1	no	—
514	C₂×D₄₇	—	2	1	no	—
515	C₂×D₄₇	—	2	1	no	—
516	C₂×D₄₇	—	2	1	no	—
517	C₂×D₄₇	—	2	1	no	—
518	C₂×D₄₇	—	2	1	no	—
519	C₂×D₄₇	—	2	1	no	—
520	C₂×D₄₇	—	4	2	no	—
521	C₂×D₄₇	—	4	2	no	—
522	C₂×D₄₇	—	4	2	no	—
523	C₂×D₄₇	—	4	2	no	—
524	C₂×D₄₇	—	4	2	no	—
525	C₂×D₄₇	—	4	2	no	—
526	C₂×D₄₇	—	8	8	no	—
527	C₂×D₄₇	—	16	4	no	—
528	C₂×D₄₇	#576	1	2	yes	—
529	C₄×C₄₇	—	2	1	no	—
530	C₄×C₄₇	—	2	1	no	—
531	C₄×C₄₇	—	2	1	no	—
532	C₄×C₄₇	—	2	1	no	—
533	C₄×C₄₇	—	2	1	no	—
534	C₄×C₄₇	—	2	1	no	—
535	C₄×C₄₇	—	4	2	no	—
536	C₄×C₄₇	—	4	2	no	—
537	C₄×C₄₇	—	4	2	no	—
538	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
539	C₄×C₄₇	#585	1	1	yes	characteristic
540	Dic₄₇	—	2	1	no	—
541	Dic₄₇	—	2	1	no	—
542	Dic₄₇	—	2	1	no	—
543	Dic₄₇	—	2	1	no	—
544	Dic₄₇	—	2	1	no	—
545	Dic₄₇	—	4	2	no	—
546	Dic₄₇	—	4	2	no	—
547	#3513	—	47	2	no	—
548	#3396	—	47	1	no	—
549	#3380	D₄₇	1	1	yes	characteristic, complemented
550	#3370	—	47	2	no	—
551	#3339	—	47	1	no	—
552	#3336	—	47	1	no	—
553	#3334	—	47	1	no	—
554	#3322	—	47	2	no	—
555	#3310	—	47	2	no	—
556	#3306	—	47	2	no	—
557	#3280	—	47	1	no	—
558	#3280	—	47	1	no	—
559	D₄×D₈	—	47	1	no	—
560	#3176	—	47	1	no	—
561	#3175	—	47	1	no	—
562	#3168	—	47	1	no	—
563	#3119	—	47	2	no	—
564	#3118	—	47	2	no	—
565	#3114	—	47	2	no	—
566	#2966	—	47	1	no	—
567	#2951	—	47	1	no	—
568	#2948	—	47	1	no	—
569	C₂×C₄×D₈	—	47	1	no	—
570	C₂×C₄₇	—	4	4	no	—
571	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
572	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
573	C₂×C₄₇	#3584	1	1	yes	characteristic
574	D₄₇	—	2	2	no	—
575	D₄₇	—	4	1	no	—
576	D₄₇	—	4	1	no	—
577	D₄₇	—	8	2	no	—
578	D₄₇	—	8	2	no	—
579	C₂×#135	—	47	1	no	—
580	C₂²×D₈	—	47	1	no	—
581	C₂²×D₈	—	47	1	no	—
582	#559	—	47	2	no	—
583	#554	C₂×D₄₇	1	2	yes	complemented
584	#553	—	47	2	no	—
585	#553	—	94	2	no	—
586	#552	—	47	2	no	—
587	#551	—	94	2	no	—
588	#551	—	94	2	no	—
589	#547	—	47	2	no	—
590	#546	—	47	2	no	—
591	#546	—	47	2	no	—
592	#546	—	94	2	no	—
593	D₄²	—	47	2	no	—
594	#542	—	47	2	no	—
595	#540	—	47	2	no	—
596	#539	—	94	2	no	—
597	#538	—	94	2	no	—
598	#529	—	47	1	no	—
599	#529	—	47	2	no	—
600	#525	—	94	2	no	—
601	C₂×#123	—	94	2	no	—
602	#520	—	47	2	no	—
603	#518	—	47	2	no	—
604	C₂×C₄×D₄	—	47	2	no	—
605	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
606	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
607	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
608	#495	—	47	1	no	—
609	#495	—	47	1	no	—
610	#493	—	47	1	no	—
611	#490	—	47	2	no	—
612	#489	—	47	2	no	—
613	#488	—	47	2	no	—
614	#485	—	47	2	no	—
615	#483	—	47	2	no	—
616	#482	—	47	2	no	—
617	#481	—	47	2	no	—
618	#480	—	47	2	no	—
619	#480	—	47	2	no	—
620	#479	—	47	2	no	—
621	#478	—	47	2	no	—
622	#478	C₂×D₄₇	1	2	yes	complemented
623	#478	C₂×D₄₇	1	2	yes	complemented
624	#476	C₂×D₄₇	1	2	yes	complemented
625	#474	—	47	2	no	—
626	#469	—	47	2	no	—
627	#468	—	47	2	no	—
628	#467	—	47	1	no	—
629	#467	—	47	1	no	—
630	#466	—	47	1	no	—
631	#466	—	47	1	no	—
632	#466	—	47	1	no	—
633	#466	—	47	1	no	—
634	#465	—	47	2	no	—
635	#463	—	47	2	no	—
636	#463	—	47	2	no	—
637	#463	—	47	2	no	—
638	#463	—	47	2	no	—
639	#460	—	47	2	no	—
640	#459	—	47	2	no	—
641	#450	—	47	2	no	—
642	#450	—	47	2	no	—
643	#449	—	47	2	no	—
644	#449	—	47	2	no	—
645	#447	—	47	2	no	—
646	#447	—	47	2	no	—
647	#446	—	47	1	no	—
648	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
649	#442	—	47	2	no	—
650	#442	—	47	2	no	—
651	#442	—	47	2	no	—
652	#440	—	47	2	no	—
653	#440	—	47	2	no	—
654	#440	—	47	2	no	—
655	C₄×Q₁₆	—	47	1	no	—
656	C₄×Q₁₆	—	47	1	no	—
657	C₄×SD₁₆	—	47	2	no	—
658	C₄×D₈	—	47	1	no	—
659	C₄×D₈	—	47	2	no	—
660	C₄×D₈	—	47	1	no	—
661	C₄×D₈	—	47	1	no	—
662	C₄×D₈	—	47	2	no	—
663	C₄×D₈	—	47	1	no	—
664	C₄×D₈	—	47	1	no	—
665	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
666	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
667	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
668	#436	—	47	1	no	—
669	#435	—	47	1	no	—
670	#435	—	47	1	no	—
671	C₈×D₄	—	47	1	no	—
672	C₈×D₄	—	47	1	no	—
673	C₈×D₄	—	47	1	no	—
674	#433	—	47	1	no	—
675	#433	—	47	1	no	—
676	#432	—	47	1	no	—
677	#427	—	47	1	no	—
678	C₂×#107	—	47	1	no	—
679	C₂×#107	—	47	1	no	—
680	#418	—	47	2	no	—
681	#417	—	47	2	no	—
682	C₂×#102	—	47	2	no	—
683	#405	—	47	1	no	—
684	#405	—	47	1	no	—
685	C₂×C₄×C₈	—	47	1	no	—
686	C₄₇	#61471	1	1	yes	characteristic, complemented, Sylow
687	C₂×#41	—	47	2	no	—
688	C₂×#41	—	94	2	no	—
689	C₂²×D₄	—	47	2	no	—
690	C₂²×D₄	—	47	2	no	—
691	C₂²×D₄	—	94	2	no	—
692	C₂³×C₄	—	94	2	no	—
693	#135	—	94	4	no	—
694	C₂×Q₁₆	—	47	1	no	—
695	C₂×SD₁₆	—	47	2	no	—
696	C₂×SD₁₆	—	47	2	no	—
697	C₂×SD₁₆	—	47	2	no	—
698	C₂×D₈	—	47	2	no	—
699	C₂×D₈	—	47	2	no	—
700	C₂×D₈	—	47	1	no	—
701	C₂×D₈	—	47	1	no	—
702	C₂×D₈	—	47	2	no	—
703	C₂×D₈	—	94	4	no	—
704	C₂×D₈	—	94	4	no	—
705	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
706	C₂×M₁₆	—	47	1	no	—
707	C₂×M₁₆	—	47	1	no	—
708	C₂²×C₈	—	47	1	no	—
709	C₂²×C₈	—	47	1	no	—
710	C₂²×C₈	—	47	1	no	—
711	C₂²×C₈	—	47	1	no	—
712	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
713	#127	—	47	2	no	—
714	#126	—	47	1	no	—
715	#126	—	47	1	no	—
716	#126	—	94	2	no	—
717	#126	—	94	2	no	—
718	#126	—	94	2	no	—
719	#126	—	94	2	no	—
720	#125	—	47	1	no	—
721	#125	—	94	2	no	—
722	#125	C₂²×D₄₇	1	2	yes	—
723	#125	C₂²×D₄₇	1	2	yes	—
724	#124	—	47	1	no	—
725	#124	—	47	2	no	—
726	#124	—	47	2	no	—
727	#124	—	94	2	no	—
728	#124	—	94	2	no	—
729	#123	—	47	1	no	—
730	#123	—	47	1	no	—
731	#123	—	94	2	no	—
732	#123	—	94	2	no	—
733	#123	—	94	2	no	—
734	#123	—	94	2	no	—
735	#123	—	94	2	no	—
736	#123	—	94	2	no	—
737	#123	—	94	2	no	—
738	#123	—	94	2	no	—
739	#123	—	94	2	no	—
740	#123	—	94	2	no	—
741	#123	—	94	2	no	—
742	#123	—	94	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	47	1	no	—
747	C₂²⋊Q₈	—	47	2	no	—
748	C₂²⋊Q₈	—	47	2	no	—
749	C₂²⋊Q₈	—	94	2	no	—
750	C₂²⋊Q₈	—	94	2	no	—
751	#121	—	47	1	no	—
752	#121	—	47	2	no	—
753	#121	—	47	2	no	—
754	#121	—	47	2	no	—
755	#121	—	47	2	no	—
756	#121	—	94	2	no	—
757	#121	—	94	2	no	—
758	#121	—	94	2	no	—
759	#121	—	94	2	no	—
760	#121	—	94	2	no	—
761	#121	—	94	2	no	—
762	#120	—	94	2	no	—
763	#120	—	94	2	no	—
764	#120	—	94	2	no	—
765	#120	—	94	2	no	—
766	C₄×Q₈	—	47	2	no	—
767	C₄×Q₈	—	47	2	no	—
768	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
769	C₄×D₄	—	47	2	no	—
770	C₄×D₄	—	47	2	no	—
771	C₄×D₄	—	47	2	no	—
772	C₄×D₄	—	47	1	no	—
773	C₄×D₄	—	47	1	no	—
774	C₄×D₄	—	47	1	no	—
775	C₄×D₄	—	47	2	no	—
776	C₄×D₄	—	47	2	no	—
777	C₄×D₄	—	94	2	no	—
778	C₄×D₄	—	94	2	no	—
779	C₄×D₄	—	94	2	no	—
780	C₄×D₄	—	94	2	no	—
781	C₄×D₄	—	94	2	no	—
782	C₄×D₄	—	94	2	no	—
783	C₄×D₄	—	94	2	no	—
784	C₄×D₄	—	94	2	no	—
785	C₄×D₄	—	94	2	no	—
786	C₄×D₄	C₂²×D₄₇	1	2	yes	—
787	C₄×D₄	C₂²×D₄₇	1	2	yes	—
788	C₄×D₄	C₂²×D₄₇	1	2	yes	—
789	#117	—	47	1	no	—
790	#117	—	47	1	no	—
791	#117	—	47	2	no	—
792	#117	—	94	2	no	—
793	#117	—	94	2	no	—
794	#117	—	94	2	no	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	—	47	2	no	—
797	C₂×C₄⋊C₄	—	47	2	no	—
798	C₂×C₄⋊C₄	—	94	2	no	—
799	C₂×C₂²⋊C₄	—	94	2	no	—
800	C₂×C₂²⋊C₄	—	94	2	no	—
801	C₂×C₂²⋊C₄	—	94	2	no	—
802	C₂×C₂²⋊C₄	—	94	2	no	—
803	C₂×C₂²⋊C₄	—	94	2	no	—
804	C₂×C₄²	—	47	1	no	—
805	#107	—	47	1	no	—
806	#107	—	47	2	no	—
807	#107	—	47	2	no	—
808	#107	C₂²×D₄₇	1	1	yes	characteristic
809	#107	C₂²×D₄₇	1	1	yes	characteristic
810	#107	C₂²×D₄₇	1	1	yes	characteristic
811	#107	C₂²×D₄₇	1	2	yes	—
812	#106	—	47	2	no	—
813	#106	C₂²×D₄₇	1	2	yes	—
814	#106	C₂²×D₄₇	1	2	yes	—
815	C₄⋊C₈	—	47	1	no	—
816	C₄⋊C₈	—	47	1	no	—
817	C₄⋊C₈	—	47	1	no	—
818	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
819	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
820	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
821	#103	—	47	2	no	—
822	#103	—	47	2	no	—
823	#103	—	47	2	no	—
824	#103	—	47	2	no	—
825	#102	—	47	2	no	—
826	#102	—	47	2	no	—
827	#102	—	47	2	no	—
828	#102	—	47	2	no	—
829	#102	—	47	2	no	—
830	#102	—	47	2	no	—
831	#102	—	47	2	no	—
832	#102	—	47	2	no	—
833	#102	—	47	2	no	—
834	#102	C₂²×D₄₇	1	2	yes	—
835	#102	C₂²×D₄₇	1	2	yes	—
836	#102	C₂²×D₄₇	1	2	yes	—
837	C₂²⋊C₈	—	47	1	no	—
838	C₂²⋊C₈	—	47	1	no	—
839	C₂²⋊C₈	—	47	1	no	—
840	C₂²⋊C₈	—	47	1	no	—
841	C₂²⋊C₈	—	47	1	no	—
842	C₂²⋊C₈	—	47	1	no	—
843	#97	—	47	1	no	—
844	#97	—	47	1	no	—
845	#97	—	47	1	no	—
846	#97	—	47	1	no	—
847	C₄×C₈	—	47	1	no	—
848	C₄×C₈	—	47	1	no	—
849	C₄×C₈	—	47	1	no	—
850	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
851	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
852	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
853	C₂⁴	—	94	2	no	—
854	C₂⁴	—	94	2	no	—
855	#41	—	94	4	no	—
856	#41	—	376	4	no	—
857	#41	—	188	2	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	47	2	no	—
860	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
861	C₂×D₄	—	47	1	no	—
862	C₂×D₄	—	47	1	no	—
863	C₂×D₄	—	47	1	no	—
864	C₂×D₄	—	47	2	no	—
865	C₂×D₄	—	47	2	no	—
866	C₂×D₄	—	94	2	no	—
867	C₂×D₄	—	94	2	no	—
868	C₂×D₄	—	94	2	no	—
869	C₂×D₄	—	94	2	no	—
870	C₂×D₄	—	94	2	no	—
871	C₂×D₄	—	94	2	no	—
872	C₂×D₄	—	94	4	no	—
873	C₂×D₄	—	94	4	no	—
874	C₂×D₄	—	94	2	no	—
875	C₂×D₄	—	94	2	no	—
876	C₂×D₄	—	94	2	no	—
877	C₂×D₄	—	376	4	no	—
878	C₂×D₄	—	188	2	no	—
879	C₂×D₄	—	188	2	no	—
880	C₂×D₄	C₂³×D₄₇	1	2	yes	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	47	1	no	—
885	C₂²×C₄	—	47	1	no	—
886	C₂²×C₄	—	47	1	no	—
887	C₂²×C₄	—	47	1	no	—
888	C₂²×C₄	—	47	1	no	—
889	C₂²×C₄	—	94	2	no	—
890	C₂²×C₄	—	94	2	no	—
891	C₂²×C₄	—	94	2	no	—
892	C₂²×C₄	—	94	2	no	—
893	C₂²×C₄	—	94	2	no	—
894	C₂²×C₄	—	94	2	no	—
895	C₂²×C₄	—	94	2	no	—
896	C₂²×C₄	—	94	2	no	—
897	C₂²×C₄	—	376	4	no	—
898	Q₁₆	—	94	2	no	—
899	SD₁₆	—	94	4	no	—
900	SD₁₆	—	188	2	no	—
901	SD₁₆	—	188	2	no	—
902	D₈	—	94	4	no	—
903	D₈	—	94	4	no	—
904	D₈	—	94	2	no	—
905	D₈	—	94	2	no	—
906	D₈	—	188	2	no	—
907	D₈	#10625354	1	4	yes	complemented
908	M₁₆	—	188	1	no	—
909	M₁₆	—	188	1	no	—
910	C₂×C₈	—	47	1	no	—
911	C₂×C₈	—	47	1	no	—
912	C₂×C₈	—	47	1	no	—
913	C₂×C₈	—	47	1	no	—
914	C₂×C₈	—	94	2	no	—
915	C₂×C₈	—	94	2	no	—
916	C₂×C₈	—	94	2	no	—
917	C₂×C₈	—	188	1	no	—
918	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
919	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
920	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
921	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	47	1	no	—
928	C₄⋊C₄	—	47	1	no	—
929	C₄⋊C₄	—	47	1	no	—
930	C₄⋊C₄	—	47	1	no	—
931	C₄⋊C₄	—	47	1	no	—
932	C₄⋊C₄	—	47	1	no	—
933	C₄⋊C₄	—	47	1	no	—
934	C₄⋊C₄	—	47	2	no	—
935	C₄⋊C₄	—	94	2	no	—
936	C₄⋊C₄	—	94	2	no	—
937	C₄⋊C₄	—	94	2	no	—
938	C₄⋊C₄	—	94	2	no	—
939	C₄⋊C₄	—	94	2	no	—
940	C₄⋊C₄	—	94	2	no	—
941	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
942	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
943	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
944	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
945	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
946	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	47	1	no	—
951	C₂²⋊C₄	—	47	1	no	—
952	C₂²⋊C₄	—	47	1	no	—
953	C₂²⋊C₄	—	47	1	no	—
954	C₂²⋊C₄	—	47	1	no	—
955	C₂²⋊C₄	—	47	1	no	—
956	C₂²⋊C₄	—	47	1	no	—
957	C₂²⋊C₄	—	47	1	no	—
958	C₂²⋊C₄	—	47	1	no	—
959	C₂²⋊C₄	—	47	1	no	—
960	C₂²⋊C₄	—	94	2	no	—
961	C₂²⋊C₄	—	94	2	no	—
962	C₂²⋊C₄	—	94	2	no	—
963	C₂²⋊C₄	—	94	2	no	—
964	C₂²⋊C₄	—	94	2	no	—
965	C₂²⋊C₄	—	94	2	no	—
966	C₂²⋊C₄	—	94	2	no	—
967	C₂²⋊C₄	—	94	2	no	—
968	C₂²⋊C₄	—	94	2	no	—
969	C₂²⋊C₄	—	94	2	no	—
970	C₂²⋊C₄	—	94	2	no	—
971	C₂²⋊C₄	—	94	2	no	—
972	C₂²⋊C₄	—	94	2	no	—
973	C₂²⋊C₄	—	94	2	no	—
974	C₂²⋊C₄	—	94	2	no	—
975	C₂²⋊C₄	—	94	2	no	—
976	C₄²	—	47	1	no	—
977	C₄²	—	47	1	no	—
978	C₄²	—	47	1	no	—
979	C₄²	—	94	2	no	—
980	C₄²	—	94	2	no	—
981	C₄²	—	94	2	no	—
982	C₄²	C₂³×D₄₇	1	1	yes	characteristic
983	C₄²	C₂³×D₄₇	1	1	yes	characteristic
984	C₄²	C₂³×D₄₇	1	1	yes	characteristic
985	C₂³	—	2	2	no	—
986	C₂³	—	47	1	no	—
987	C₂³	—	47	1	no	—
988	C₂³	—	47	1	no	—
989	C₂³	—	94	2	no	—
990	C₂³	—	94	2	no	—
991	C₂³	—	376	2	no	—
992	C₂³	—	376	2	no	—
993	C₂³	—	376	2	no	—
994	C₂³	—	188	4	no	—
995	C₂³	—	188	4	no	—
996	C₂³	—	188	4	no	—
997	Q₈	—	4	1	no	—
998	Q₈	—	8	2	no	—
999	Q₈	—	94	2	no	—
1000	Q₈	—	94	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	94	2	no	—
1003	D₄	—	94	2	no	—
1004	D₄	—	94	2	no	—
1005	D₄	—	94	2	no	—
1006	D₄	—	94	2	no	—
1007	D₄	—	94	2	no	—
1008	D₄	—	376	2	no	—
1009	D₄	—	376	2	no	—
1010	D₄	—	376	2	no	—
1011	D₄	—	376	2	no	—
1012	D₄	—	376	2	no	—
1013	D₄	—	188	1	no	—
1014	D₄	—	188	4	no	—
1015	D₄	—	188	4	no	—
1016	D₄	—	188	4	no	—
1017	D₄	—	188	4	no	—
1018	D₄	C₂×#10625354	1	4	yes	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	47	1	no	—
1026	C₂×C₄	—	47	1	no	—
1027	C₂×C₄	—	47	1	no	—
1028	C₂×C₄	—	47	1	no	—
1029	C₂×C₄	—	47	1	no	—
1030	C₂×C₄	—	94	2	no	—
1031	C₂×C₄	—	94	1	no	—
1032	C₂×C₄	—	94	1	no	—
1033	C₂×C₄	—	94	1	no	—
1034	C₂×C₄	—	94	1	no	—
1035	C₂×C₄	—	94	1	no	—
1036	C₂×C₄	—	94	1	no	—
1037	C₂×C₄	—	94	2	no	—
1038	C₂×C₄	—	94	2	no	—
1039	C₂×C₄	—	376	2	no	—
1040	C₂×C₄	—	376	2	no	—
1041	C₂×C₄	—	376	2	no	—
1042	C₂×C₄	—	376	2	no	—
1043	C₂×C₄	—	376	2	no	—
1044	C₂×C₄	—	376	2	no	—
1045	C₂×C₄	—	188	1	no	—
1046	C₂×C₄	—	188	4	no	—
1047	C₂×C₄	—	188	4	no	—
1048	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1049	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1050	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1051	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1052	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1053	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1054	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	94	1	no	—
1059	C₈	—	94	1	no	—
1060	C₈	—	94	1	no	—
1061	C₈	—	94	1	no	—
1062	C₈	C₂×#10625354	1	2	yes	—
1063	C₂²	—	2	4	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	47	2	no	—
1067	C₂²	—	94	1	no	—
1068	C₂²	—	94	1	no	—
1069	C₂²	—	94	1	no	—
1070	C₂²	—	94	1	no	—
1071	C₂²	—	94	1	no	—
1072	C₂²	—	94	1	no	—
1073	C₂²	—	94	1	no	—
1074	C₂²	—	94	1	no	—
1075	C₂²	—	376	8	no	—
1076	C₂²	—	188	2	no	—
1077	C₂²	—	188	2	no	—
1078	C₂²	—	188	2	no	—
1079	C₂²	—	188	2	no	—
1080	C₂²	—	188	2	no	—
1081	C₂²	—	188	2	no	—
1082	C₂²	—	752	4	no	—
1083	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	94	1	no	—
1094	C₄	—	94	1	no	—
1095	C₄	—	94	1	no	—
1096	C₄	—	94	1	no	—
1097	C₄	—	94	1	no	—
1098	C₄	—	188	2	no	—
1099	C₄	—	188	2	no	—
1100	C₄	C₂²×#10625354	1	1	yes	characteristic
1101	C₄	#15689960	1	1	yes	characteristic
1102	C₂	—	4	4	no	—
1103	C₂	—	94	2	no	—
1104	C₂	—	376	2	no	—
1105	C₂	—	376	2	no	—
1106	C₂	—	188	1	no	—
1107	C₂	—	188	1	no	—
1108	C₂	D₄×#10625354	1	1	yes	characteristic
1109	C₂	#576×D₄₇	1	1	yes	characteristic
1110	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3380	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3380	D₄₇
hypocenter	C₄₇	#61471
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3380

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20257331	C₂	semidirect
2. #20256401	C₂	semidirect
3. #20256141	C₂	semidirect
4. #20255789	C₂	semidirect
5. #20255755	C₂	semidirect
6. #20255735	C₂	semidirect
7. #20255586	C₂	semidirect
8. #20255406	C₂	semidirect
9. #20255346	C₂	semidirect
10. #20255074	C₂	semidirect
11. #20255074	C₂	semidirect
12. D₈×D₁₈₈	C₂	semidirect
13. #20254039	C₂	semidirect
14. #20254030	C₂	semidirect
15. #20253960	C₂	semidirect
16. #20253592	C₂	semidirect
17. #20253577	C₂	semidirect
18. #20253531	C₂	semidirect
19. #20252365	C₂	semidirect
20. #20252258	C₂	semidirect
21. #20252235	C₂	semidirect
22. C₄×D₈×D₄₇	C₂	semidirect
23. C₄₇×#3380	C₂	semidirect
27. #15689858	C₂²	semidirect
28. #15689826	C₂²	semidirect
33. #15689776	C₂²	semidirect
34. #15689768	C₂²	semidirect
35. #15689768	C₂²	semidirect
38. #15689747	C₂²	semidirect
39. #15689729	C₂²	semidirect
43. #15689658	C₂²	semidirect
46. #15689602	C₂²	semidirect
47. #15689595	C₂²	semidirect
48. C₄×D₄×D₄₇	C₂²	semidirect
49. #15689507	C₂²	semidirect
50. #15689507	C₂²	semidirect
52. #15689489	C₂²	semidirect
53. #15689485	C₂²	semidirect
54. #15689480	C₂²	semidirect
55. #15689467	C₂²	semidirect
56. #15689455	C₂²	semidirect
57. #15689449	C₂²	semidirect
58. #15689443	C₂²	semidirect
59. #15689438	C₂²	semidirect
60. #15689438	C₂²	semidirect
61. #15689427	C₂²	semidirect
62. #15689420	C₂²	semidirect
63. #15689400	C₂²	semidirect
64. #15689377	C₂²	semidirect
65. #15689370	C₂²	semidirect
66. #15689365	C₂²	semidirect
67. #15689365	C₂²	semidirect
70. #15689360	C₂²	semidirect
71. #15689360	C₂²	semidirect
72. #15689353	C₂²	semidirect
73. #15689339	C₂²	semidirect
74. #15689339	C₂²	semidirect
75. #15689338	C₂²	semidirect
76. #15689338	C₂²	semidirect
77. #15689324	C₂²	semidirect
79. #15689275	C₂²	semidirect
80. #15689275	C₂²	semidirect
81. #15689269	C₂²	semidirect
82. #15689269	C₂²	semidirect
85. #15689254	C₂²	semidirect
86. #15689234	C₂²	semidirect
87. #15689233	C₂²	semidirect
88. #15689232	C₂²	semidirect
89. #15689223	C₂²	semidirect
90. #15689222	C₂²	semidirect
91. #15689220	C₂²	semidirect
92. C₄×Dic₁₈₈	C₂²	semidirect
93. #15689217	C₂²	semidirect
94. #15689210	C₂²	semidirect
95. C₄×D₃₇₆	C₂²	semidirect
96. C₄×D₃₇₆	C₂²	semidirect
98. #15689205	C₂²	semidirect
99. #15689205	C₂²	semidirect
100. C₄×#10625334	C₂²	semidirect
101. #15689203	C₂²	semidirect
102. #15689200	C₂²	semidirect
104. #15689193	C₂²	semidirect
106. C₈×D₁₈₈	C₂²	semidirect
107. C₈×D₁₈₈	C₂²	semidirect
108. #15689183	C₂²	semidirect
109. #15689183	C₂²	semidirect
110. #15689179	C₂²	semidirect
111. #15689160	C₂²	semidirect
112. #107×D₄₇	C₂²	semidirect
113. #107×D₄₇	C₂²	semidirect
114. #15689126	C₂²	semidirect
115. #15689121	C₂²	semidirect
116. #102×D₄₇	C₂²	semidirect
117. #15689077	C₂²	semidirect
118. #15689077	C₂²	semidirect
119. C₄×C₈×D₄₇	C₂²	semidirect
120. C₄₇×#554	C₂²	semidirect
121. C₄₇×#500	C₂²	semidirect
122. C₄₇×#499	C₂²	semidirect
123. C₄₇×#499	C₂²	semidirect
124. C₄₇×#478	C₂²	semidirect
125. C₄₇×#478	C₂²	semidirect
126. C₄₇×#476	C₂²	semidirect
127. C₈×Q₈×C₄₇	C₂²	semidirect
342. D₈×C₄₇	#41	semidirect
549. #3380	D₄₇	semidirect
583. #554	C₂×D₄₇	semidirect
605. #500	C₂×D₄₇	semidirect
606. #499	C₂×D₄₇	semidirect
607. #499	C₂×D₄₇	semidirect
622. #478	C₂×D₄₇	semidirect
623. #478	C₂×D₄₇	semidirect
624. #476	C₂×D₄₇	semidirect
648. C₈×Q₈	C₂×D₄₇	semidirect
686. C₄₇	#61471	semidirect
907. D₈	#10625354	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20257331	2
#20256401	2
#20256141	2
#20255789	2
#20255755	2
#20255735	2
#20255586	2
#20255406	2
#20255346	2
#20255074	2
D₈×D₁₈₈	2
#20254039	2
#20254030	2
#20253960	2
#20253592	2
#20253577	2
#20253531	2
#20252365	2
#20252258	2
#20252235	2
C₄×D₈×D₄₇	2
C₄₇×#3380	2
#61471	47